There are many goods for which quantity supplied (QS) does not match up with quantity demanded (QD). Some of them are like this because of government intervention in markets, but others are that way because the suppliers want them to be.
One possible good for which QS is less than QD is oil refineries. There are those who argue that gas prices would be lower if the government would allow more refineries to come into existence more easily. The government imposes stringent safety regulations, thereby making it harder for refineries to open.
Another example of goods for which QS is higher than QD is tickets to the concerts of really big stars. These tickets are scarce for two main reasons. First, it is simply impossible for these stars to put on the number of concerts that their fans would like. They would not be capable of performing that constantly. Second, the artists want there to be a tight market for the tickets. They want to be seen as commodities. If they put on as many shows as their fans would like, the prices of their tickets would drop and they would no longer seem like such big stars. In these two cases, the government is not at fault. Instead, it is simply the nature of the good in question and the ability and desire of the suppliers to produce that good.